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Let f : A → B and g : B → C. For each statement below...

Let f : A → B and g : B → C. For each statement below either prove it or construct f, g, A, B, C which show that the statement is false.

(a) If g ◦ f is surjective, then g is surjective.

(b) If g ◦ f is surjective, then f is surjective.

(c) If g ◦ f is injective, then f and g are injective

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